Finished, suppressing irritation though it had been severely jeopardised (10)
I believe the answer is:
endangered
'jeopardised' is the definition.
('endanger' can be a synonym of 'jeopardize')
'finished suppressing irritation' is the wordplay.
'finished' becomes 'ended' (similar in meaning).
'suppressing' is an insertion indicator.
'irritation' becomes 'anger'.
'ended' enclosing 'anger' is 'ENDANGERED'.
'though it had been severely' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for endangered that I've seen before include "Like some species" , "Vulnerable" , "Threatened" , "in a perilous situation" , "put at risk" .)